3 * fast mathematics routines.
7 * A Fast, Compact Approximation of the Exponential Function
9 * IDSIA, Lugano, Switzerland
10 * http://www.inf.ethz.ch/~schraudo/pubs/exp.pdf
12 * Fast log() Function, by Laurent de Soras:
13 * http://www.flipcode.com/cgi-bin/msg.cgi?showThread=Tip-Fastlogfunction&forum=totd&id=-1
22 #define _SG_FMATH_HXX 1
25 # error This library requires C++
29 #define _USE_MATH_DEFINES
34 double fast_exp(double val);
35 double fast_exp2(const double val);
37 float fast_pow(const float val1, const float val2);
38 float fast_log2(const float cal);
39 float fast_root(const float f, const int n);
41 float _fast_pow2(const float cal);
42 float _fast_log2(const float val);
44 float fast_sin(const float val);
45 float fast_cos(const float val);
46 float fast_tan(const float val);
47 float fast_asin(const float val);
48 float fast_acos(const float val);
49 float fast_atan(const float val);
51 void fast_BSL(float &x, register unsigned long shiftAmount);
52 void fast_BSR(float &x, register unsigned long shiftAmount);
55 inline float fast_log2 (float val)
57 int * const exp_ptr = reinterpret_cast <int *> (&val);
59 const int log_2 = ((x >> 23) & 255) - 128;
64 val = ((-1.0f/3) * val + 2) * val - 2.0f/3; // (1)
71 * This function is about 3 times faster than the system log() function
72 * and has an error of about 0.01%
74 inline float fast_log (const float &val)
76 return (fast_log2 (val) * 0.69314718f);
79 inline float fast_log10 (const float &val)
81 return (fast_log2(val) / 3.321928095f);
86 * This function is about twice as fast as the system pow(x,y) function
88 inline float fast_pow(const float val1, const float val2)
90 return _fast_pow2(val2 * _fast_log2(val1));
95 * Haven't seen this elsewhere, probably because it is too obvious?
96 * Anyway, these functions are intended for 32-bit floating point numbers
97 * only and should work a bit faster than the regular ones.
99 inline float fast_abs(float f)
101 int i=((*(int*)&f)&0x7fffffff);
102 return (*(float*)&i);
105 inline float fast_neg(float f)
107 int i=((*(int*)&f)^0x80000000);
108 return (*(float*)&i);
111 inline int fast_sgn(float f)
113 return 1+(((*(int*)&f)>>31)<<1);
116 #endif // !_SG_FMATH_HXX